Algorithmic Number Theory
Lattices, Number Fields, Curves and Cryptography
Edited by Joseph P. Buhler and Peter Stevenhagen
Contents
Front matter (front page, copyright page)
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Table of Contents
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Preface, ix-x
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Solving the Pell equation by Hendrik W. Lenstra, Jr., 1-23
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Basic algorithms in number theory by Joe Buhler and Stan Wagon, 25-68
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Smooth numbers and the quadratic sieve by Carl Pomerance, 69-81
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The number field sieve by Peter Stevenhagen, 83-100
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Four primality testing algorithms by René Schoof, 101-126
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Lattices by Hendrik W. Lenstra, Jr., 127-181
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Elliptic curves by Bjorn Poonen, 183-207
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The arithmetic of number rings by Peter Stevenhagen, 209-266
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Smooth numbers: computational number theory and beyond by Andrew Granville, 267-323
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Fast multiplication and its applications by Daniel J. Bernstein, 325-384
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Elementary thoughts on discrete logarithms by Carl Pomerance, 385-396
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The impact of the number field sieve on the discrete logarithm problem in finite fields
by Oliver Schirokauer, 397-420
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Reducing lattice bases to find small-height values of univariate polynomials
by Daniel J. Bernstein, 421-446
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Computing Arakelov class groups by René Schoof, 447-495
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Computational class field theory by Henri Cohen and Peter Stevenhagen, 497-534
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Protecting communications against forgery by Daniel J. Bernstein, 535-549
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Algorithmic theory of zeta functions over finite fields by Daqing Wan, 551-578
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Counting points on varieties over finite fields of small characteristic
by Alan G. B. Lauder and Daqing Wan, 579-612
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Congruent number problems and their variants by Jaap Top and Noriko Yui, 613-639
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An introduction to computing modular forms using modular symbols by William A. Stein, 641-652
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